Question

A small business owner visits her bank to ask for a loan. The owner states that she can repay a loan at $1,300 per month for the next three years and then $2,600 per month for two years after that. If the bank is charging customers 8.25 percent APR, how much would it be willing to lend the business owner? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

Bank would be willing to lend the business owner $ 86,141.35

Working:

Bank would be willing to lend so much amount so that present value of monthly repayment is equal to loan amount.
Step-1:Present value of monthly repayment of next 3 years
Present value	=	Monthly repayment * Present value of annuity of 1
	=	$         1,300	*	31.794659
	=	$ 41,333.06
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.006875)^-36)/0.006875		i	8.25%/12	=	0.006875
	=	31.794659		n	3*12	=	36
Step-2:Present value of monthly repayment of balance years
Present Value	=	Monthly loan repayment * Present value of annuity of 1 * Present value of 1
	=	$         2,600	*	22.0549002	*	0.781412
	=	$ 44,808.29
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.006875)^-24)/0.006875		i	8.25%/12	=	0.006875
	=	22.0549002		n	2*12	=	24
Present value of 1	=	(1+i)^-n		Where,
	=	(1+0.006875)^-36		i	8.25%/12	=	0.006875
	=	0.78141172		n	3*12	=	36
Step-3:Calculation of loan amount
Loan amount	=	Present value of monthly repayments
	=	$ 41,333.06	+	$ 44,808.29
	=	$ 86,141.35